An accurate and parameter‐free analysis for the converse Poynting effect in large constrained torsion of highly elastic soft tubes

Abstract

New exact solutions to large constrained torsion of highly elastic soft tubes are obtained from a new hyper‐elastic constitutive model. This new model is established with a new form of the multiaxial elastic potential toward simultaneously matching multiple data sets for three benchmark modes, including the uniaxial extension of a bar, the equi‐biaxial extension of a thin plate and the plane‐strain extension of a plate strip. With the new model, exact closed‐form solutions to the stress responses for these benchmark modes are first derived and shown to be of decoupled nature, and, then, an accurate analysis for the converse Poynting effect of twisted highly elastic tubes with fixed ends is presented with a new technique in treating nonlinear coupling complexities. The main novelties are incorporated as follows. First, multiple data sets for three benchmark modes can be accurately and automatically matched with no need to identify any unknown parameters; next, the nonlinear coupled system of the governing equations for four variables in a twisted tube, including the averaged radius and the wall‐thickness as well as the axial constrained stress and the shear stress, can be reduced to treating a single nonlinear equation; and, accordingly, the nonlinear coupling complexities can be worked out and exact results are obtainable.